How do you find partial derivatives of a function, find critical points and second partial derivatives.?

Answer 1

in getting partial derivative, you should consider only one variable, all others can be considered constants.
critical point, equate the first derivative to zero, solve for the variable.

Answer 2

When you have a function in terms of so many variables, you take derivative of the function in one variable. This is called partial derivative of a function.
For example, you have a function f(x,y,z)
you take the derivative of the function in one variable:
df(x,y,z)/dx : a derivative of the function
df(x,y,z)/dy : a derivative of the function
df(x,y,z)/dz : a derivative of the function

Second partial derivatives of the function:
You take the derivatives of the derivative function.

Let's say
g(x,y,z)=df(x,y,z)/dx

Let's take the derivative of g(x,y,z) in y
dg(x,y,z)/dy=h(x,y,z) : This is the secon derivative of the function

h(x,y,z)=d^2f(x,y,z)/dxdy

Answer 3

at the same time as u r calculating fx u might want to guage y as a consonant and vice versa: fx=2x-4y=0 fy=-4x+3y^2+4=0 from the first equation u have x=2y and through fixing x contained in the 2d equation and fixing it u'll have the answer. -8y+3y^2+4=0 a million/3 (3y-6)(3y-2) =0 (y-2)(3y-2)=0 y=2, y=3/2 and from the first equation we would have: x=4, x=3 (4,2) (3,3/2) for the 2d: d(ex)/dx=ex d(siny)/dy=dy/dx * comfortable so fx=ex siny fy=dy/dx ex comfortable

Answer 4

It would be better if you asked the solution to a particular problem rather than ask for pages of theory.